Bounded integral control for uncertain ISS systems with convex input constraints

Abstract

In this paper, a new Bounded Integral Controller (BIC) is proposed to replace the conventional Integral Control (IC) for regulating uncertain Input-to-State Stable (ISS) nonlinear systems and additionally ensuring that the control input evolution remains within a prescribed compact convex set for all time. This is particularly important for controlling multi-input systems with uncertainties or unknown dynamics/parameters and handling input constraints that introduce couplings between the control input elements forming a specific compact and convex set. Given this set, the proposed BIC takes a suitable nonlinear dynamic form and employing ISS and invariant set theory, it is analytically proven that the trajectory of the entire control input vector will remain within the desired set independently of the plant dynamic structure or parameters. Contrary to the original BIC and its recent extensions, which either limit the control input elements independently or restrict them within a ball set (Euclidean norm bound), the proposed approach may constrain the input evolution within any given compact convex set, thus leading to a generalisation of the original BIC. In order to illustrate the theoretical analysis of the proposed BIC and compare its performance with respect to the conventional methods, one academic and two realistic examples from the area of robotics and power systems are investigated using a simulated underwater robot and a power converter in an experimental platform, respectively, each introducing different input constraints.